A VRF is a Virtual Routing/Forwarding instance. In other words, a "mini routing table" that's isolated from all the others.

While it comes from MPLS VPNs, you can use it without MPLS entirely. This is called VRF-Lite. And basically what it does is disables the requirement for an MBGP back-end to exist. So you'll just have some interfaces with Cust-A, some with Cust-B, etc. And each operates in their own little world without regard/care for anyone else.